An Introduction to Stochastic ModelingServing as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition:
|
Contents
|
Chapter 1 Introduction
|
1 |
|
Chapter 2 Conditional Probability and Conditional Expectation
|
47 |
|
Introduction
|
79 |
|
Chapter 4 The Long Run Behavior of Markov Chains
|
165 |
|
Chapter 5 Poisson Processes
|
223 |
|
Chapter 6 Continuous Time Markov Chains
|
277 |
|
Chapter 7 Renewal Phenomena
|
347 |
|
Chapter 8 Brownian Motion and Related Processes
|
391 |
|
Chapter 9 Queueing Systems
|
447 |
|
Chapter 10 Random Evolutions
|
495 |
|
Chapter 11 Characteristic Functions and Their Applications
|
525 |
| 541 | |
|
Answers to Exercises
|
543 |
| 557 | |
Other editions - View all
Common terms and phrases
according analysis arrival assume average begins Brownian motion calculations called Chapter component conditional Consider constant continuous corresponding cost customers death process defined denote density function derive Determine distribution function distribution with parameter duration equal equation evaluate event example Exercises exists expected exponentially distributed expression failure Figure first fixed formula fraction given gives identically independent individual initial integral interval length limiting limiting distribution long run Markov chain mean observed obtain occurs operating particles period Poisson distribution Poisson process population positive possible Pr{X Problems proof queue random variable renewal process replacement respectively result sample server Show single solution standard starting stationary step stochastic successive Suppose takes Theorem tion transition probability matrix unit variance waiting zero